Solve for x -4/5x=16/15

$- \frac{4}{5} x = \frac{16}{15}$

Step 1

Multiply both sides of the equation by $- \frac{5}{4}$ .

$- \frac{5}{4} (- \frac{4}{5} x) = - \frac{5}{4} \cdot \frac{16}{15}$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{4} (- \frac{4}{5} x)$ .

Combine $x$ and $\frac{4}{5}$ .

$- \frac{5}{4} (- \frac{x \cdot 4}{5}) = - \frac{5}{4} \cdot \frac{16}{15}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{- 5}{4} (- \frac{x \cdot 4}{5}) = - \frac{5}{4} \cdot \frac{16}{15}$

Move the leading negative in $- \frac{x \cdot 4}{5}$ into the numerator.

$\frac{- 5}{4} \cdot \frac{- x \cdot 4}{5} = - \frac{5}{4} \cdot \frac{16}{15}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{4} \cdot \frac{- x \cdot 4}{5} = - \frac{5}{4} \cdot \frac{16}{15}$

Cancel the common factor.

$\frac{5 \cdot - 1}{4} \cdot \frac{- x \cdot 4}{5} = - \frac{5}{4} \cdot \frac{16}{15}$

Rewrite the expression.

$\frac{- 1}{4} (- x \cdot 4) = - \frac{5}{4} \cdot \frac{16}{15}$

Cancel the common factor of $4$ .

Factor $4$ out of $- x \cdot 4$ .

$\frac{- 1}{4} (4 \cdot (- x)) = - \frac{5}{4} \cdot \frac{16}{15}$

Cancel the common factor.

$\frac{- 1}{4} (4 \cdot (- x)) = - \frac{5}{4} \cdot \frac{16}{15}$

Rewrite the expression.

$- - x = - \frac{5}{4} \cdot \frac{16}{15}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{4} \cdot \frac{16}{15}$

Multiply $x$ by $1$ .

$x = - \frac{5}{4} \cdot \frac{16}{15}$

Simplify the right side.

Simplify $- \frac{5}{4} \cdot \frac{16}{15}$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$x = \frac{- 5}{4} \cdot \frac{16}{15}$

Factor $5$ out of $- 5$ .

$x = \frac{5 (- 1)}{4} \cdot \frac{16}{15}$

Factor $5$ out of $15$ .

$x = \frac{5 \cdot - 1}{4} \cdot \frac{16}{5 \cdot 3}$

Cancel the common factor.

$x = \frac{5 \cdot - 1}{4} \cdot \frac{16}{5 \cdot 3}$

Rewrite the expression.

$x = \frac{- 1}{4} \cdot \frac{16}{3}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$x = \frac{- 1}{4} \cdot \frac{4 (4)}{3}$

Cancel the common factor.

$x = \frac{- 1}{4} \cdot \frac{4 \cdot 4}{3}$

Rewrite the expression.

$x = - \frac{4}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$

Solve for x -4/5x=16/15

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